Semi-infinite Circular Pipe Research Articles

Comparing the end correction of a spherically baffled piston to infinitely baffled and unbaffled circular radiators (L).

Models of acoustical systems commonly employ end corrections to represent the radiation impedance of a vibrating element. Although several analytic solutions appear in the literature, the end corrections of an infinitely baffled circular piston and an unbaffled semi-infinite circular pipe remain popular in modeling applications. This Letter compares the end correction of these two configurations to that of a radially vibrating cap on a sphere. The results show that the spherically baffled end correction, when expressed as a function of spherical-cap radius, falls between these two extremal boundary conditions.

Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition

Space-time evolution of a flow in a semi-infinite circular pipe {x⩾0,y2+z2⩽R2} is investigated via direct numerical simulations. The unsteady turbulent inflow velocity u∣x=0 is extracted from a streamwise-periodic auxiliary simulation. It is shown that at t≫0 spatially evolving flow does not depend on initial state u∣t=0. It takes the form of spatially periodic flow of the auxiliary simulation with superimposed spatially growing perturbation. The amplitude of the perturbation increases exponentially with distance from the inlet. The growth rate is estimated for the considered Reynolds number. The obtained results suggest that the memory of the inflow boundary condition in spatial simulations is evident for a significant distance from the inlet. In the considered case an almost periodic flow is established (with less than 1% relative deviation from the periodicity) over a distance as large as 70 pipe radii.

Numerical calculation of the split function for a sound field around a semi-infinite circular pipe in the Wiener-Hopf technique

Numerical calculation of the split function for a sound field around a semi-infinite circular pipe in the Wiener-Hopf technique

Analysis of inviscid vortex breakdown in a semi-infinite pipe

Axisymmetric vortex breakdown in a steady, inviscid, incompressible flow in a semi-infinite circular pipe is considered analytically. We suggest a new perception of vortex breakdown and compare ours with other approaches. In our view, vortex breakdown occurs due to solution nonuniqueness in some range of inflow parameters when the entire steady flow experiences a jump to another metastable steady state with the same boundary conditions. These co-existing solutions are smooth along the pipe length; they have the same mechanical energy but, in general, different flow forces. Vortex breakdown necessarily occurs by a continuous change in flow parameters (usually the swirl number) when the solution fails to exist (locally) because of fold or similar catastrophe, but spontaneous jumps (in some range of parameters) between different metastable solutions (not on a fold) can also be caused by large flow perturbations. The folds can appear due to transcritical bifurcation, which is destroyed (in the case considered here) by the injection of azimuthal vorticity into the vortex core at the pipe entrance. A high level of the entrance swirl leads to separation zones (even for solid-body inflow!) where the steady flow is undetermined. We find that the nonuniqueness interval in parameter space is connected with the flow pattern inside the separation zone. We consider models for dealing with two such flow patterns: the traditional analytic continuation (leading to a recirculation zone) and a new stagnant separation zone model. We reveal serious defects of the analytic continuation approach. The stagnation zone model is superior in that solutions always exist and, for large enough inflow swirl, exhibit nonuniqueness and folds, thus explaining the experimentally observed hysteretic jump transitions in vortex breakdown. We also predict some new phenomena, which deserve experimental investigation.

管壁から流入する半無限円管内の流れ

The steady-state incompressible laminar flow in a semi-infinite circular pipe with uniform injection or suction through the porous wall has been investigated. The present analysis simulates also the flow field produced by the burning of inner surface of cyindrical grain in a solid rocket motor. A similar solution of fully non-linear form of the Navier-Stokes equation is calculated numerically. The properties of flow such as velocity components are obtained as functions of injection parameter R=aV/ν. The region near the closed end has been analyzed numerically by means of the finite difference method, and the results is used to inspect the similar solution. It is found that the flow is not similar near the closed end, and that the effect of viscosity of solid end has been confined to the narrow region of x/a<2.

Sound radiation from a semi-infinite circular pipe having an arbitrary profile of orifice

A general solution for the sound radiated from a circular pipe having an arbitrary inside profile of orifice is obtained by the use of Laplace transforms and the Wiener–Hopf technique. The pipe may include vibrating surfaces. Results are calculated for the velocity potential at a large distance from the orifice and for the reflection coefficient for the dominant-mode component of the velocity potential in the pipe. The solution is applicable, for example, to the design of an acoustic transducer, and for noise control from the orifice. Some numerical results for the velocity potential of a model loudspeaker and for the excess attenuation of a muffler near the open end of a pipe are presented graphically. Subject Classification:[43]20.55, [43]20.15.

Radiating Gas Flow of a Large Optical Thickness along a Semi-Infinite Circular Pipe

A theoretical study is made on a grey radiating gas flow along a semiinfinite circular pipe when the global optical thickness is large. The radiave heat transfer is assumed to be of the same order of magnitude as the convective one. Analyses are carried out up to the first two orders of expansion with respect to the inverse square root of the Bouguer number. The first order solution and the solution including the effect due to the radiation slip coincide with those of a flow those of a flow past a semi-infinite flat plate. For the flow outside the pipe, a correction is made on the solution taking into account the effect due to the wall curvature. In the flow inside the pipe, the effects due to the pressure change and the compressibility of the gas appear in addition to the effect due to the wall curvature.

Comparison of Ray Theory with Exact Theory for Scattering by Open Wave Guides

The exact solutions for electromagnetic scattering by a semi-infinite parallel plane wave guide and by a semi-infinite circular pipe are expanded asymptotically for wave guide dimensions large compared to wavelength. Attention is confined to the diffracted field at observation points well away from shadow boundaries and reflection boundaries. The results yield term by term comparisons with the corresponding results derived by means of ray theory. The simple ray method does not yield complete agreement with the asymptotic forms of the exact solutions.